Randomized algorithms for synthesis of switching rules for multimodal systems

IEEE Transactions on Automatic Control

Volumn 50, Issue 6, 2005, Pages 754-767

  Ishii, Hideaki ^a   Başar, Tamer ^b   Tempo, Roberto ^c  

^a UNIVERSITY OF TOKYO   (Japan)

^b University of Illinois at Urbana Champaign   (United States)

^c POLITECNICO DI TORINO   (Italy)

Author keywords

Multiple Lyapunov function; Nonconvexity; Randomized algorithms; Switched systems; Switching rule design

Indexed keywords

ALGORITHMS; ASYMPTOTIC STABILITY; COMPUTATIONAL COMPLEXITY; CONVERGENCE OF NUMERICAL METHODS; GRADIENT METHODS; LYAPUNOV METHODS; PROBABILITY; SWITCHING; SYSTEM STABILITY;

MULTIPLE LYAPUNOV FUNCTION; NONCONVEXITY; RANDOMIZED ALGORITHMS; SWITCHING RULE DESIGN;

CONTROL SYSTEM SYNTHESIS;

EID: 21344441668     PISSN: 00189286     EISSN: None     Source Type: Journal    
DOI: 10.1109/TAC.2005.849187     Document Type: Article

References (26)

1. A.V. Aho, J. E. Hopcroft, and J. D. Ullman, Data Structures and Algorithms. Reading, MA: Addison-Wesley, 1983.
2. R. B. Ash, Real Analysis and Probability. New York: Academic, 1972.
3. V. D. Blondel and J. N. Tsitsiklis, "A survey of computational complexity results in systems and control," Automatica, vol. 36, pp. 1249-1274, 2000.
4. S. Boyd, L. El Ghaoui, E. Ferron, and V. Balakrishnan, Linear Matrix Inequalities in System and Control Theory. Philadelphia, PA: SIAM, 1994, vol. 15, SIAM Studies in Applied Mathematics.
5. M. S. Branicky, "Multiple Lyapunov functions and other analysis tools for switched and hybrid systems," IEEE Trans. Autom. Control, vol. 43, no. 4, pp. 475-482, Apr. 1998.
6. G. Calafiore and B. T. Polyak, "Stochastic algorithms for exact and approximate feasibility of robust LMIs," IEEE Trans. Autom. Control, vol. 46, no. 6, pp. 1755-1759, Nov. 2001.
7. R. DeCarlo, M. S. Branicky, S. Pettersson, and B. Lennartson, "Perspectives and results on the stability and stabilizability of hybrid systems," Proc. IEEE, vol. 88, no. 7, pp. 1069-1082, Jul. 2000.
8. E. Feron, "Quadratic stabilizability of switched systems via state and output feedback," MIT Center for Intelligent Control Systems, Cambridge, MA, Tech. Rep. CICS-P-468, 1996.
9. Y. Fujisaki, F. Dabbene, and R. Tempo, "Probabilistic design of LPV control systems," Automatica, vol. 39, pp. 1323-1337, 2003.
10. K.-C. Goh, M. G. Safonov, and J. H. Ly, "Robust synthesis via bilinear matrix inequalities," Int. J. Rob. Nonlinear Control, vol. 6, pp. 1079-1095, 1996.
11. H. Ishii, T. Başar, and R. Tempo, "Randomized algorithms for quadratic stability of quantized sampled-data systems," Automatica, vol. 40, pp. 839-846, 2004.
12. M. Johansson and A. Rantzer, "Computation of piecewise quadratic Lyapunov functions for hybrid systems," IEEE Trans. Autom. Control, vol. 43, no. 4, pp. 555-559, Apr. 1998.
13. S. Kanev, B. De Schutter, and M. Verhaegen, "An ellipsoid algorithm for probabilistic robust controller design," Syst. Control Lett., vol. 49, pp. 365-375, 2003.
14. H. J. Kushner and G. G. Yin, Stochastic Approximation and Recursive Algorithms and Applications. New York: Springer-Verlag, 2003.
15. D. Liberzon, Switching in Systems and Control. Boston, MA: Birkhäuser, 2003.
16. D. Liberzon and R. Tempo, "Common Lyapunov functions and gradient algorithms," IEEE Trans. Autom. Control, vol. 49, no. 6, pp. 990-994, Jun. 2004.
17. J. Malmborg, B. Bernhardsson, and K. J. Åström, "A stabilizing switching scheme for multi controller systems," in Proc. 13th IFAC World Congr., 1996, pp. 229-234.
18. Y. Oishi, "Probabilistic design of a robust state-feedback controller based on parameter-dependent Lyapunov functions," in Proc. 42nd Conf. Decision and Control, 2003, pp. 1920-1925.
19. Y. Oishi and H. Kimura, "Computational complexity of randomized algorithms for solving parameter-dependent linear matrix inequalities," Automatica, vol. 39, pp. 2149-2156, 2003.
20. P. M. Pardalos and J. B. Rosen, Constrained Global Optimization: Algorithms and Applications. Berlin, Germany: Springer-Verlag, 1987, vol. 268, Lecture Notes on Computer Science.
21. B. T. Polyak and R. Tempo, "Probabilistic robust design with linear quadratic regulators," Syst. Control Lett., vol. 43, pp. 343-353, 2001.
22. R. Tempo, G. Calafiore, and F. Dabbene, Randomized Algorithms for Analysis and Control of Uncertain Systems. London, U.K.: Springer-Verlag, 2004.
23. M. Vidyasagar, "Statistical learning theory and randomized algorithms for control," IEEE Control Syst. Mag., vol. 18, no. 6, pp. 69-85, Jun. 1998.
24. M. Wicks and R. DeCarlo, "Solution of coupled Lyapunov equations for the stabilization of multimodal linear systems," in Proc. Amer. Control Conf., 1997, pp. 1709-1713.
25. L. Xie, S. Shishkin, and M. Fu, "Piecewise lyapunov functions for robust stability of linear time-varying systems," Syst. Control Lett., vol. 31, pp. 165-171, 1997.
26. H. Ye, A. N. Michel, and L. Hou, "Stability theory for hybrid dynamical systems," IEEE Trans. Autom. Control, vol. 43, no. 4, pp. 461-474, Apr. 1998.